another one I am having trouble with involves simplifying expressions with negative exponents. Can anyone help

Question

This is the problem I am having a really hard time with. I appreciate everyone's help.

3x^3y^4z^-2 / 6x^-1y^3z^-3

I am also still having a hard time with these:

7. (25x3)^2/3 / (125xy2)^1/3

9. (2s + 5z)2 (s + 3z)2

Divide
10. (2x^3-x^2+3x-1) / (x+2)

Please help me. I am in an on-line school and I have just a couple of weeks left with this class. I barely use math (which is why I am bad) and this is my last math class. Please help!!!!!

Answer 1

Remember; x^(-b) = 1/(x^b)
(x^a)(x^b) = x^(a+b)
(x^a)/(x^b) = (x^a)(x^(-b)) = x^(a-b)
and of course, x^1 = x

3x^3y^4z^-2 / 6x^-1y^3z^-3 =
(3/6) x^3y^4z^-2 / x^-1y^3z^-3 =
(3/6) x^3 y^4 z^(-2) (x^1y^-3z^3) =
(1/2) x^3 x^1 y^4 y^-3 z^(-2) z^3 =
(1/2) x^(3+1) y^(4-3) z^(-2-3) =
(1/2) x^4 y^1 z^(-5) =
(1/2) x^4 y /z^(-5)
which we can also write as
x^4 y /(2z^5)

Answer 2

(3x^3y^4z^-2) / (6x^-1y^3z^-3)
= (3x^3y^4/z^2) / (6y^3/xz^3)
= 3x^3y^4/z^2) * (xz^3/6y^3)
= x^4yz/2

7. (25x3)^2/3 / (125xy2)^1/3
= (25^2/3 x^2)/ 5x^1/3y^2/3
= [5 cuberoot (5) x^5/3]/y^2/3

9. (2s + 5z)^2 (s + 3z)^2
= (4s^2 +10sz+25z^2)(s^2+6sz+9z^2)
= Multiply the above two trinomials for answer

10. (2x^3-x^2+3x-1) / (x+2)
= 2x^2 -5x +13 -26/(x+2)